## 1. Introduction

Stochastic rainfall models have evolved through numerous forms ranging from paired exponential density functions representing dry and wet periods of an alternating renewal process (Gabriel and Neumann, 1962; Green, 1964), to Poisson cluster models, hidden Markov models, and pulse-based models (including Bartlett–Lewis and Neyman–Scott rectangular pulse models, as described by Velghe *et al.*, 1994; Cowpertwait, 1994; Cowpertwait, 1995; Onof and Wheater, 1993; Onof and Wheater, 1994). While the range of historical applications for these models is broad (Stern and Coe, 1984), there is an increasing recognition of their suitability for resolving spatial and temporal scale discrepancies between ‘output’ (such as precipitation and temperature dynamics) from general circulation and regional climate models (GCMs and RCMs, for details see Lofgren *et al.*, 2002; Holman *et al.*, 2012) and the input required by decision-support, process-based models (the Great Lakes Advanced Hydrologic Prediction System, described in Gronewold *et al.*, 2011a, is one example). The spatial extent and temporal resolution of RCM simulations, however, rarely corresponds directly to the input requirements of these regional and local-scale models, additional examples of which include hydrological models (Beven, 2001; Wagener and Wheater, 2006), terrestrial pollutant fate and transport models (Ferguson *et al.*, 2003), and water quality models (Reckhow, 1999; Grant *et al.*, 2001), which often run at an hourly or daily time step over a specific watershed or subbasin (for further discussion, see Bates *et al.*, 1998; Chapman, 1998; Fowler *et al.*, 2007; Burton *et al.*, 2008; Timbal *et al.*, 2009).

Burton *et al.* (2008) and Chapman (1998) note that despite advances in stochastic rainfall simulation models, including improvements in model performance, there is a need for efficient, robust model calibration routines that explicitly acknowledge parameter uncertainty, correlation, and model error, and propagate those features into rainfall simulations. To begin to bridge this research gap we evaluate the performance of an exponential-dispersion rainfall simulation model (EDM, for details see Dunn, 2004) using a Bayesian Markov chain Monte Carlo (MCMC) routine (Berry, 1996; Bolstad, 2004; Gelman *et al.*, 2004). A variety of modelling approaches and distributional forms have been explored for simulating rainfall including censored quantile regression (Friederichs and Hense, 2007), generalized linear models (Furrer and Katz, 2007) and Bernoulli-gamma and zero-inflated models (Haylock *et al.*, 2006; Cannon, 2008; Fernandes *et al.*, 2009), each with some advantages and limitations in their practical application. We suspect our evaluation of benefits associated with explicitly quantifying uncertainty in the EDM and, subsequently, assessing EDM skill in light of that uncertainty, will benefit a wide range of rainfall simulation modelling applications, including (but not limited to) recent applications of the EDM (see, for example, Hasan and Dunn, 2010; Hasan and Dunn, 2011a; Hasan and Dunn, 2011b).

We demonstrate our proposed modelling framework by applying the EDM to precipitation data over a series of subbasins of the North American Laurentian Great Lakes (for the remainder of this paper, we refer to precipitation in terms of equivalent rainfall). We calibrate the model to data from even-numbered years from 1969 to 2008, and then compare the predictive distribution of daily rainfall statistics representing rainfall magnitude and occurrence to data from odd-numbered years.